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All discussion below is archived from the Wikispaces export in its original unaltered form.
Please do not add any new discussion to this archive page.
All new discussion should go on Talk:Height.

Applied to chords?

Are height formulas applied to chords, too? Or is this called something different?

Erlich talks about Sethares "dissonance" measure not really being dissonance because 4:5:6 and 1/4:1/5:1/6 measure the same but the major chord sounds more consonant than the minor, so he calls it "roughness" only, and it must be combined with "tonalness" (similarity to a harmonic series) to estimate a total "consonance".

"Unlike roughness, tonalness is not merely concerned with pairwise interactions of tones but three-way and higher interactions as well. A mathematical model for it is out of my grasp at the moment."

But 1/4:1/5:1/6 = 10:12:15, which *is* in the harmonic series (like every JI chord) but farther away from the root, so some kind of height function on the chord ratios would seem to fit the "tonalness" criteria.

- Omegatron September 10, 2014, 06:54:17 AM UTC-0700